A Survey of the Differential Forms in Algebraic Singularities for N-Dimensions Number

Exploring the Use of Differential Forms in Algebraic Singularities for N-Dimensional Analysis

Abstract

The present work comprises of the study of algebraic singularities of the differential of degree (n-1) without zero on one assortment of n measurements. Martinet J.71 Studies the main idea of it in the year 1979 and we introduced idea of singularities with applications. Differential forms are a rich source of invariants in algebraic Singularities. This approach was very successful for smooth varieties, but the singular case is less well understood. We explain how the use of the h-topology (introduced by Suslin and Voevodsky in order to study motives) gives a very good object also in the singular case, at least in characteristic zero. We also explain problems and solutions in positive characteristic. Differential forms originally show up when integrating or differentiating on manifolds. The object has very many important uses. The one we are concentrating on is as a source of invariants used in order to classify varieties. This approach was very successful for smooth varieties, but the singular case is less well-understood.